1. Field of the Invention
The present invention relates to a method of manufacturing a photomask having a mask pattern on a transparent substrate and, more particularly, to a method of manufacturing a photomask in which the transmittance of a transparent substrate changes depending on the position. The present invention also relates to a semiconductor device manufacturing method using a photomask manufactured by this method.
2. Description of the Related Art
Along with the recent advance in the micropatterning of semiconductor devices, a demand for micropatterning in the photolithography process is increasing. The design rule of leading-edge devices has already reduced the half pitch (hp) to 45 nm. An exposure technique using both immersion exposure and polarization illumination manages to cope with this micropatterning.
Under the circumstances, the dimensional uniformity required for a photomask is increasingly becoming stricter to the degree that the in-plane uniformity of the mask pattern dimensions must be 2 nm (3σ). To correct the mask pattern dimensions, a technique of changing the transmittance of a quartz substrate is available. This technique decreases the transmittance of quartz at a relatively large opening of the mask pattern within the mask plane. This allows an exposure apparatus to actually transfer a pattern having substantially desired dimensions onto a wafer. One approach capable of decreasing the transmittance of the quartz substrate is to form a fine heterogeneous layer in the substrate using a femto second laser to scatter exposure light by this heterogeneous layer (e.g., see A2 in PCT [WO] 2005/008333).
This approach adjusts the transmittance change amount of the quartz substrate while maintaining the relationship with the mask in-plane dimensional distribution constant. More specifically, this approach defines the transmittance change amount as 1% when the dimensions on the mask are shifted from a desired value by 1 nm, and maintains this relationship between the dimensions on the mask and the transmittance constant within the mask plane. That is, this approach decreases by 3% the transmittance of quartz at an opening that is larger than a desired value of the dimensions on the mask by 3 nm.
The relationship between the dimensions on the mask and the transmittance (to be referred to as the transmittance correction coefficient hereinafter) is generally adjusted for a finest pattern called a cell portion. However, it has begun to be understood that since not only fine patterns but also rough patterns are present on the mask, the adjustment of the transmittance correction coefficient for the cell portion results in overcorrection in some regions. This is because a finer pattern suffers a larger dimensional fluctuation on the wafer relative to the dimensional fluctuation on the mask, and therefore has a larger value of a so-called mask error enhancement factor (MEF).
The MEF is given by:MEF=(mask magnification)×(dimensional fluctuation on wafer)/(dimensional fluctuation on mask).  (1)
As the current wafer exposure apparatus adopts ¼ reduction transfer, the mask magnification is normally 4. When a pattern to be transferred is sufficiently larger than the exposure wavelength, the MEF becomes almost 1. In this case, the dimensional fluctuation on the wafer is equivalent to ¼ that on the mask. This is because the wafer exposure apparatus adopts ¼ reduction transfer.
However, the recent lithography process of forming a micropattern equal to or smaller than the exposure wavelength uses an MEF of 2 or more to be more sensitive to the dimensional fluctuation on the mask. For example, a fine pattern need only undergo transmittance correction by 1% per nm, while a rough pattern need only undergo transmittance correction by 0.5% per nm. Hence, the adjustment of the transmittance correction coefficient for a fine pattern results in overcorrection of a rough pattern.
As described above, the conventional method of changing the transmittance of a quartz substrate to correct the pattern dimensions of a mask cannot accurately correct the transmittance because the MEF value changes depending on the pattern dimensions.